FRW barotropic zero modes: Dynamical systems observability

The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dynamical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmologyComment: 10 pages, 0 figure

High-gain nonlinear observer for simple genetic regulation process

High-gain nonlinear observers occur in the nonlinear automatic control theory and are in standard usage in chemical engineering processes. We apply such a type of analysis in the context of a very simple one-gene regulation circuit. In general, an observer combines an analytical differential-equation-based model with partial measurement of the system in order to estimate the non-measured state variables. We use one of the simplest observers, that of Gauthier et al., which is a copy of the original system plus a correction term which is easy to calculate. For the illustration of this procedure, we employ a biological model, recently adapted from Goodwin's old book by De Jong, in which one plays with the dynamics of the concentrations of the messenger RNA coding for a given protein, the protein itself, and a single metabolite. Using the observer instead of the metabolite, it is possible to rebuild the non-measured concentrations of the mRNA and the proteinComment: 9 pages, one figur

Application of multifractal wavelet analysis to spontaneous fermentation processes

An algorithm is presented here to get more detailed information, of mixed culture type, based exclusively on the biomass concentration data for fermentation processes. The analysis is performed with only the on-line measurements of the redox potential being available. It is a two-step procedure which includes an Artificial Neural Network (ANN) that relates the redox potential to the biomass concentrations in the first step. Next, a multifractal wavelet analysis is performed using the biomass estimates of the process. In this context, our results show that the redox potential is a valuable indicator of microorganism metabolic activity during the spontaneous fermentation. In this paper, the detailed design of the multifractal wavelet analysis is presented, as well as its direct experimental application at the laboratory levelComment: 12 pages, 3 figures, Physica A, to appea

PI-controlled bioreactor as a generalized Lienard system

It is shown that periodic orbits can occur in Cholette's bioreactor model working under the influence of a PI-controller. We find a diffeomorphic coordinate transformation that turns this controlled enzymatic reaction system into a generalized Lienard form. Furthermore, we give sufficient conditions for the existence and uniqueness of limit cycles in the new coordinates. We also perform numerical simulations illustrating the possibility of the existence of a local center (period annulus). A result with possible practical applications is that the oscillation frequency is a function of the integral control gain parameterComment: 15 pages, 5 figures, accepted version at Computers & Chem. En

Supersymmetric free-damped oscillators: Adaptive observer estimation of the Riccati parameter

A supersymmetric class of free damped oscillators with three parameters has been obtained in 1998 by Rosu and Reyes through the factorization of the Newton equation. The supplementary parameter is the integration constant of the general Riccati solution. The estimation of the latter parameter is performed here by employing the recent adaptive observer scheme of Besancon et al., but applied in a nonstandard form in which a time-varying quantity containing the unknown Riccati parameter is estimated first. Results of computer simulations are presented to illustrate the good feasibility of this approach for a case in which the estimation is not easily accomplished by other meansComment: 8 pages, 6 figure

Inferring mixed-culture growth from total biomass data in a wavelet approach

It is shown that the presence of mixed-culture growth in batch fermentation processes can be very accurately inferred from total biomass data by means of the wavelet analysis for singularity detection. This is accomplished by considering simple phenomenological models for the mixed growth and the more complicated case of mixed growth on a mixture of substrates. The main quantity provided by the wavelet analysis is the Holder exponent of the singularity that we determine for our illustrative examples. The numerical results point to the possibility that Holder exponents can be used to characterize the nature of the mixed-culture growth in batch fermentation processes with potential industrial applications. Moreover, the analysis of the same data affected by the common additive Gaussian noise still lead to the wavelet detection of the singularities although the Holder exponent is no longer a useful parameterComment: 17 pages and 10 (png) figure

Nonlinear software sensor for monitoring genetic regulation processes with noise and modeling errors

Nonlinear control techniques by means of a software sensor that are commonly used in chemical engineering could be also applied to genetic regulation processes. We provide here a realistic formulation of this procedure by introducing an additive white Gaussian noise, which is usually found in experimental data. Besides, we include model errors, meaning that we assume we do not know the nonlinear regulation function of the process. In order to illustrate this procedure, we employ the Goodwin dynamics of the concentrations [B.C. Goodwin, Temporal Oscillations in Cells, (Academic Press, New York, 1963)] in the simple form recently applied to single gene systems and some operon cases [H. De Jong, J. Comp. Biol. 9, 67 (2002)], which involves the dynamics of the mRNA, given protein, and metabolite concentrations. Further, we present results for a three gene case in co-regulated sets of transcription units as they occur in prokaryotes. However, instead of considering their full dynamics, we use only the data of the metabolites and a designed software sensor. We also show, more generally, that it is possible to rebuild the complete set of nonmeasured concentrations despite the uncertainties in the regulation function or, even more, in the case of not knowing the mRNA dynamics. In addition, the rebuilding of concentrations is not affected by the perturbation due to the additive white Gaussian noise and also we managed to filter the noisy output of the biological systemComment: 21 pages, 7 figures; also selected in vjbio of August 2005; this version corrects a misorder in the last three references of the published versio